Basic properties
| Modulus: | \(8007\) | |
| Conductor: | \(2669\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(52\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2669}(4,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8007.dd
\(\chi_{8007}(4,\cdot)\) \(\chi_{8007}(64,\cdot)\) \(\chi_{8007}(268,\cdot)\) \(\chi_{8007}(370,\cdot)\) \(\chi_{8007}(718,\cdot)\) \(\chi_{8007}(769,\cdot)\) \(\chi_{8007}(1024,\cdot)\) \(\chi_{8007}(1126,\cdot)\) \(\chi_{8007}(1942,\cdot)\) \(\chi_{8007}(2002,\cdot)\) \(\chi_{8007}(2359,\cdot)\) \(\chi_{8007}(3073,\cdot)\) \(\chi_{8007}(3124,\cdot)\) \(\chi_{8007}(3379,\cdot)\) \(\chi_{8007}(3481,\cdot)\) \(\chi_{8007}(4288,\cdot)\) \(\chi_{8007}(4297,\cdot)\) \(\chi_{8007}(4696,\cdot)\) \(\chi_{8007}(5716,\cdot)\) \(\chi_{8007}(5920,\cdot)\) \(\chi_{8007}(6022,\cdot)\) \(\chi_{8007}(6643,\cdot)\) \(\chi_{8007}(7051,\cdot)\) \(\chi_{8007}(7654,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{52})$ |
| Fixed field: | Number field defined by a degree 52 polynomial |
Values on generators
\((5339,1414,7855)\) → \((1,-i,e\left(\frac{21}{26}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 8007 }(4, a) \) | \(1\) | \(1\) | \(e\left(\frac{5}{13}\right)\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{29}{52}\right)\) | \(e\left(\frac{51}{52}\right)\) | \(e\left(\frac{2}{13}\right)\) | \(e\left(\frac{49}{52}\right)\) | \(e\left(\frac{45}{52}\right)\) | \(1\) | \(e\left(\frac{19}{52}\right)\) | \(e\left(\frac{7}{13}\right)\) |